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arXiv · 1504.06686

The Deeper Roles of Mathematics in Physical Laws

Kevin H. Knuth
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Abstract

Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as exemplified by the laws of physics. In this essay, I claim that much of the utility of mathematics arises from our choice of description of the physical world coupled with our desire to quantify it. This will be demonstrated in a practical sense by considering one of the most fundamental concepts of mathematics: additivity. This example will be used to show how many physical laws can be derived as constraint equations enforcing relevant symmetries in a sense that is far more fundamental than commonly appreciated.

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Kevin H. Knuth. 2015-04-25. The Deeper Roles of Mathematics in Physical Laws. https://arxiv.org/abs/1504.06686

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